Lipid bilayers are known to undergo structural changes, analogous to phase transition, as the temperature and composition are varied. Analogous structural changes occur in the membranes of living organisms and are suspected of playing a role in a number of physiological processes, such as enzyme activity, transport across membranes, anaesthetic action, cholesterol deposition, and myelin degeneration. We propose to investigate the molecular basis of these phase transitions by developing theoretical models for membranes and calculating statistical mechanical parition functions for the models. The object is to understand which molecular degrees of freedom and intermolecular interactions are primarily responsible for the phase transitions. We will investigate the following phenomena: the chain melting transition in pure phospholipid bilayers of various types of molecules, lateral phase separations in various mixtures of lipids (such as two component phospholipids and phospholipid-cholesterol mixtures) the "pretransition" in phospholipids, "molecular clustering" at temperatures above the chain melting transition, and lipid-protein organization in bilayers.